Murder on the Blackboard (1934)

They Laughed When Miss Withers Sniffed a Clue; But Kicked Themselves Ever After for Laughing

There are plenty of guilty secrets at the school where Hildegarde Withers teaches. When she finds the body of the pretty music teacher, she calls in her old friend Inspector Piper, who promptly arrests the obvious suspect. Clues multiply and everyone looks suspicious as Piper and Miss Withers continue their battle of the sexes.